function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta

s = sum(y' * log(sigmoid(X * theta)) + (1 - y)' * log(1 - sigmoid(X * theta)));

theta_tmp = theta;
theta_tmp(1) = 0;

J = -(1 / m) * s + lambda / (2*m) * (theta_tmp' * theta_tmp);

tmp = ((sigmoid(X * theta) - y)' * X / m)';
grad(1) = tmp(1);
grad(2:length(tmp)) = (tmp  + (lambda / m) .* theta)(2:length(tmp));


% =============================================================

end
